Let's break down the expression step by step.

The given expression is:

$3.9 \times 0.5 + 4 \frac{5}{6} \div 3 \frac{3}{7}$

Step 1: Multiplication

First, multiply $3.9 \times 0.5$:

$3.9 \times 0.5 = 1.95$

Step 2: Division of mixed numbers

Convert the mixed numbers into improper fractions:

• $4 \frac{5}{6} = \frac{29}{6}$
• $3 \frac{3}{7} = \frac{24}{7}$

Now, perform the division of the fractions:

$\frac{29}{6} \div \frac{24}{7} = \frac{29}{6} \times \frac{7}{24} = \frac{29 \times 7}{6 \times 24} = \frac{203}{144}$

Step 3: Add the two results

Now, add $1.95$ and $\frac{203}{144}$:

Convert $1.95$ to a fraction:

$1.95 = \frac{195}{100}$

We need a common denominator to add $\frac{195}{100}$ and $\frac{203}{144}$. The least common denominator of 100 and 144 is 720.

• Convert $\frac{195}{100}$ to have a denominator of 720:

$\frac{195}{100} = \frac{195 \times 7.2}{100 \times 7.2} = \frac{1404}{720}$

• Convert $\frac{203}{144}$ to have a denominator of 720:

$\frac{203}{144} = \frac{203 \times 5}{144 \times 5} = \frac{1015}{720}$

Now add:

$\frac{1404}{720} + \frac{1015}{720} = \frac{1404 + 1015}{720} = \frac{2419}{720}$

Final Answer:

The result in fraction form is $\frac{2419}{720}$, which is approximately:

$\frac{2419}{720} \approx 3.36$

Would you like further details or clarifications on any of these steps?

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Here are 5 follow-up questions for you to consider:

1. Can you convert the final fraction $\frac{2419}{720}$ into a mixed number?
2. How would this problem change if you replaced division with multiplication?
3. What is the decimal approximation of $\frac{29}{6} \div \frac{24}{7}$ alone?
4. What if the numbers were in scientific notation—would it be easier to solve?
5. Can you think of a real-world scenario where this calculation might be useful?

Tip: Always convert mixed numbers into improper fractions when dealing with division or multiplication problems to simplify the process.